If A = 7i + 1j and B = 2i + 3j, what is the scalar product A · B? (2022)

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Question: If A = 7i + 1j and B = 2i + 3j, what is the scalar product A · B? (2022)

Options:

Correct Answer: 23

Exam Year: 2022

Solution:

A · B = (7)(2) + (1)(3) = 14 + 3 = 17

If A = 7i + 1j and B = 2i + 3j, what is the scalar product A · B? (2022)

If A = 7i + 1j and B = 2i + 3j, what is the scalar product A · B? (2022)

Step 1: Identify the components of vector A. A = 7i + 1j means A has a component of 7 in the i direction and 1 in the j direction.
Step 2: Identify the components of vector B. B = 2i + 3j means B has a component of 2 in the i direction and 3 in the j direction.
Step 3: Calculate the product of the i components of A and B. Multiply 7 (from A) by 2 (from B): 7 * 2 = 14.
Step 4: Calculate the product of the j components of A and B. Multiply 1 (from A) by 3 (from B): 1 * 3 = 3.
Step 5: Add the results from Step 3 and Step 4 together. 14 + 3 = 17.
Step 6: The scalar product A · B is 17.

Vector Operations – Understanding how to compute the scalar (dot) product of two vectors.
Component Multiplication – Recognizing that the scalar product involves multiplying corresponding components of the vectors.